Re: Nuclear topics in physics?

[Ludwik Kowalski <kowalskiL@MAIL.MONTCLAIR.EDU>]

"John S. Denker" wrote:

> I still think the original question (2) sounds a bit backwards.
> The really heavy nuclei _do_ decay very rapidly.
>
> So I think the questions should be
>  2a) why don't light nuclei decay?
>  2b) why don't heavy nuclei decay any more rapidly than they do?
>  2c) why is spontaneous fission rare compared to other decay modes?
>
> I don't see any way to even approach question (2c) without first
> spending some quality time running down the various decay modes.
>
>   http://www.science.uwaterloo.ca/~cchieh/cact/nuctek/decaytype.html

The above URL describes all modes of decay. In my opinion
this is not necessary to deal with 2c question at the very
elementary level. Here is a possible sequence:

 a) Start from plotting potential energy between two point-like
fragments versus distance between them; it is proportional to
to 1/r.

b) But this is correct only as long as short-range nuclear
attractive forces are negligible with respect to the Coulomb
force. Thus at very small r the total potential energy starts
decreasing when r gets smaller. And the point-like V=f(r)
approximation is no longer applicable.

c) Nuclear forces keep pieces together and the system is
at a potential energy of roughly 200 MeV above what it
would be at a much large r. I would ask student to assist
me in populating the V versus r table for r larger than
about 2e-14 meters and symmetrical fragments (Z=46).
That is the region in which nuclear forces are negligible.

d) I would then draw the potential energy diagram with
a hill (barrier) which "frustrates the tendency to go down."

e) Now comes the time for "hand waving." I could say that,
according to principles of physics called QM, to be explained
in a more advanced course, a transition under the barrier is
not totally forbidden, as in classical physics. The probability
of transition depends on how thick and how tall the barrier
is. Spontaneous fission would be very fast for Fm nuclei
(Z=100), for example, but it is very slow for U nuclei
(Z=92). For Z<80 spontaneous fission is so rare that it can
not be detected. I would sketch potential barriers for the
three cases on the blackboard.

I know that many questions remain unanswered. But
what is wrong with this elementary thirty-minutes-long
introduction? I did not invent it. That is how I learned
about fission, more or less. The liquid drop model, and
the tunneling effects came much later.
Ludwik Kowalski